{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LEDJXUDKZE7H2ZEM7WGN4J3Z6Q","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6bd516bf5a2b9b3dce79e2aa6b53e0cd9d7a30554dcebb010f73b247a57cbdd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-22T11:34:13Z","title_canon_sha256":"3486f922b7d151998ebf8069c7c280302dc948747e09b719701face7c17c97fa"},"schema_version":"1.0","source":{"id":"1903.09454","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09454","created_at":"2026-05-17T23:43:32Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09454v2","created_at":"2026-05-17T23:43:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09454","created_at":"2026-05-17T23:43:32Z"},{"alias_kind":"pith_short_12","alias_value":"LEDJXUDKZE7H","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LEDJXUDKZE7H2ZEM","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LEDJXUDK","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:fc7fd0957a08b6aff55b4cefdc485449689761e4422d4b1c3a5c5bf5d4e6ecca","target":"graph","created_at":"2026-05-17T23:43:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce the arrow product, a systematic generating function technique for directed graph enumeration. It provides short proofs for previous results of Gessel on the number of directed acyclic graphs and of Liskovets, Robinson and Wright on the number of strongly connected directed graphs. We also recover Robinson's enumerative results on directed graphs where all strongly connected components belong to a given family.","authors_text":"\\'Elie de Panafieu, Sergey Dovgal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-22T11:34:13Z","title":"Symbolic method and directed graph enumeration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09454","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:045ec6af0dec95390aeffd73d743e30ed147afd236335f0f3b986a363217d27f","target":"record","created_at":"2026-05-17T23:43:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"6bd516bf5a2b9b3dce79e2aa6b53e0cd9d7a30554dcebb010f73b247a57cbdd6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-03-22T11:34:13Z","title_canon_sha256":"3486f922b7d151998ebf8069c7c280302dc948747e09b719701face7c17c97fa"},"schema_version":"1.0","source":{"id":"1903.09454","kind":"arxiv","version":2}},"canonical_sha256":"59069bd06ac93e7d648cfd8cde2779f40422c897b3a2e9007997cc1510d1e55d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59069bd06ac93e7d648cfd8cde2779f40422c897b3a2e9007997cc1510d1e55d","first_computed_at":"2026-05-17T23:43:32.741242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:32.741242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sf3FVxItBs1sLxo6xG+tKtEjTy5HjtWINCmlIPwCdphmmHWW5O6mUp3XrBRhl7WboFtTmrYHrDlefxV36J2+DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:32.741704Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09454","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:045ec6af0dec95390aeffd73d743e30ed147afd236335f0f3b986a363217d27f","sha256:fc7fd0957a08b6aff55b4cefdc485449689761e4422d4b1c3a5c5bf5d4e6ecca"],"state_sha256":"9821cf08e95132ab79a6e1163e6358fccf6be8a3b9bcc26a196d7a88a6fa2b68"}